Partial differential equations (PDEs) with constant coefficients are considered to be very practicable so that a variety of engineering problems fall within this truly mesh-free methods. In order to apply the EBFs locally a subdomain, or a so called “cloud”, is assigned to each domain node. Each cloud includes some of the domain nodes, in addition to the central one, and it does not have any compact support. The union of all clouds must cover the problem domain, and meanwhile they can overlap with each other. In this method, the unknown field variable is approximated through a series of EBFs within each cloud. The unknown coefficients of the series are evaluated in terms of the nodal degree of freedoms (DoFs). In this sense, for each subdomain an algebraic relation between the DoFs of the central node and the adjacent ones is found. Repeating the procedure for all clouds leads to the construct of the final system of equations. At the boundary nodes, a formulation similar to that of the domain nodes is applied to implement the boundary conditions. It is demonstrated that by using a regularization algorithm in the fitting process, the method can solve a variety of problems with regular and irregular point distribution defined on different domain shapes. In this study, the method is applied to different justify; MARGIN: 0cm 0cm 0pt" Keywords: Partial differential equations, Mesh-free method, Local exponential basis functions, High convergence rate, Poisson, Helmholtz, Elasticity, Convection diffusion, wave propagation, unbounded domain.
